1.3.2 Constraints, rules and parameters
OT relies on the constraint hierarchy to provide the effects ascribed in the derivational approach to rules. OT constraints present some similarities to the rules, parameters, and constraints familiar from derivational theory, as all of these concepts involve evaluating linguistic structures with regard to specified properties. As should be clear from Hayes’ (1995) treatment of foot-formation, constraints had been used in previous rule-based approaches, but were never formalized in the way that rules were. In contrast to rules, they dictated what could not happen, limiting the effect of rule-based processes that would otherwise overgenerate, producing incorrect or non-intuitive results, or prohibiting certain structures which could otherwise provide unwanted input or output representations. Constraints also motivated processes which otherwise had no impetus discernible from the rules.
One example of a constraint type used in derivational theory is McCarthy & Prince’s (1986) bimoraic constraint. This constraint is simply the codification of an observation that feet or words in the languages observed necessarily contained two moras, and the further realization that this generalization held explanatory power for the phonology. Constraining the rules, which were applied in an inherently very open-ended and powerful system, and the representations, which were similarly unlimited in regard to possible characterizations, improved the expressiveness of the phonology, although constraints did not have any formal position in the theory and were at root descriptive stipulations. They were often described in terms of "natural" conceptions of linguistic "well-formedness". Some constraints familiar from the early literature of Lexical Phonology include the Obligatory Contour Principle of Leben (1973), Kiparsky’s (1973) Elsewhere condition, and the Strict Cycle Condition of Mascar— (1976).
Parameters, introduced by Vergnaud & Halle (1978) and developed further by Hayes (1981, 1995), were similar to constraints, but were understood as varying between languages, which would each have their own "settings". Hayes used parameters to indicate, for example, foot-type and directionality of syllabification. Such parameter settings were crucial to supply information necessary to Hayes’ model of metrification. However, there was no formal way to express these parameters within the traditional formulation of phonological rules. Rather, the parameters resembled a somewhat more rigorous form of the conditions that had accompanied rules in some previous approaches. When rules were seen as having a limited, rather than universal application, conditions were appended which specified the limiting circumstances. While descriptively helpful, such appended conditions are not the ideal mechanism with which to achieve the formal explicitness demanded by the generative argument.
The term "constraint", like "rule," seems to imply universal application, and this is how constraints were typically interpreted. However, like rules, there were constraints that seemed to apply only sometimes, even within the same grammar, e.g., the extrametricality of Hayes (1987) which applies only in certain cases. Constraint-based theories, such as the "constraints and repair strategies" theory of Paradis (1988) or the "declarative phonology" of Scobbie (1991), Bird (1990) and Bird & Ellison (1992), dispensed with rules seen in earlier generative theory completely and made the constraints themselves the basis of the grammar. However, the absolute enforcement of constraints presented the many of the same problems as rule-based theories. Only the hierarchy of violable constraints of Prince & Smolensky’s (1993) Optimality Theory formally accounts for the apparent non-universality of certain rule- or constraint-based regularities. The candidate which minimally violates the constraint hierarchy (McCarthy & Prince 1994) is considered optimal and will surface. The candidate which survives the constraint evaluation is not the "perfect" candidate, but the least imperfect candidate. This ranking of violable constraints precisely captures in a fully principled manner the linguistic phenomenon first described by the classical Indian grammarian Pa–ini, and only approximated by Chomsky & Halle’s disjunctive rules and Kiparsky’s Elsewhere Condition.
Constraints in Optimality Theory not only reprise their more limited role in derivational theory, but also provide, in a unified theoretical mechanism, the functionality divided in derivational theory between rules, constraints and parameters. Like rules, they define environments, and what should appear in those environments. Like derivational constraints, they can restrict the possible set of structures which can surface. And like parameters, they can account for apparent language-specific "settings", such as the directionality of foot-formation, through references to properties of constituents, such as their edges, as in the Alignment constraints of McCarthy & Prince (1993a). The constraint hierarchy, made up of ranked, violable constraints, allows for the expression of the entire grammar while avoiding the pitfalls of universal constraints, rules and parameters, which always suffered from the previously inexplicable fact that they did not apply universally.
1.3.3 Prosodic constituents in Optimality Theory
The set of structures referred to by constraints will be limited in this study to the constituent members of grammatical hierarchies. Violable, ranked constraints describing relationships between members of these hierarchies will provide all the mechanisms necessary to produce the surface forms of the language. One such set of constituents is found in the prosodic hierarchy, which was developed in the context of derivational theory. (¤ 1.2.1) In chapter four, the OT constraints which are used to account for English stress patterns refer to the same prosodic constituents which yielded stress effects in derivational theories such as Prosodic Phonology (Nespor & Vogel 1986, Inkelas 1989) and Metrical Phonology (Prince 1983, Hayes 1981, 1982, 1995).
The prosodic hierarchy, as noted above, was originally used to model structure above the word level (Selkirk 1980, 1982a, 1984). Nespor & Vogel (1986) describe the clitic group, the phonological phrase, the intonational phrase and the intonational utterance as higher level phrasal constituents. Inkelas (1989) accepts all of these apart from the clitic group, which she believes can be replaced by one of the other phrasal categories in the languages where it purportedly appears. She also notes (p. 43) that compounds, "which form one single morphological constituent, behave as two constituents for the purpose of phonological rules." and sees compounds as iterative combinations of prosodic words.
Hayes (1995: 367) states that phrasal stress assignment is markedly different from the assignment of word stress, at least in languages where metrical structure has already been assigned to all syllables up to the word level, such as English. Stress rules at these levels usually apply an End Rule which promotes one of the prosodic word heads from the previous level. The most common type of adjustment at these levels is clash adjustment, wherein a head is demoted and an adjacent head within the same constituent is promoted due to the adjacency of a stronger stress, as seen in the th“rteen mŽn example given above, (1.2).
At the word-level and below, the relevant level for the discussion of word-stress, the prosodic word dominates the foot, syllable, and mora. This category has been defined by Selkirk (1980, 1982a, b, 1984) and Nespor & Vogel (1986) as the category which encompasses the feet it dominates.
(1.5) PrWd
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Ft
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s
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m
The word is the domain for "word stress," and the assignment of this main word stress to one of its constituent feet is accomplished in derivational studies by the application of an End Rule. End Rules usually assigned prominence to a foot on the right or left edge of the word. Although the word in Hayes’ (1995) system includes extrametrical and unfooted material, the assignment of prominence is only possible for feet, thus eliminating unfooted and extrametrical syllables from consideration for receiving word stress.
Using a prosodic system composed of the constituents and mechanisms described above, the assignment of stress to proposed lexical entries of words, in a derivational context, proceeds according to rule. Thus the assignment of stress to the word extrametricality could proceed as follows:
(1.6) Assignment of syllable structure:7
s s s s s s s
|\ | | | | | |
m m m m m m m m
| | ///| /| //| /| /| /|
e k s t r a m e t r i k a l i t i
The final syllable of such a word is extrametrical in English (according to Hayes 1982), and quantity-sensitive trochaic foot assignment proceeds from right to left. Below, using the bracketed grid notation of Hayes (1995), grid marks indicate the heads of syllables, while feet are indicated by parentheses. Syllable notation has been replaced for convenience by the segments themselves, separated by white space:
( x) ( x . ) ( x . )
(1.7) (ek) stra (me tri) (ka li)
Following Hayes (1995), the second syllable would be left unparsed, rather than creating an uneven trochee. In this work, uneven trochees will be allowed, which would result in the following parse:
( x . ) ( x . ) ( x . )
(1.8) (ek stra) (me tri) (ka li)
Finally, an End Rule which inserts a grid mark on (or promotes the head of) the rightmost constituent head yields the final prosodic word:
( x )
( x . ) ( x . ) ( x . )
(1.9) (k) stræ (m tri) (k‡ li)
In English, stressed vowels maintain their quality, while vowels in "weak" position tend to reduce to schwa, especially in open syllables.
The prosodic hierarchy provides a structural framework which allows for the representation of the relative and iterative properties associated with stress as a series of purely local relations. Alternations can be understood as occurring in the context of the prosodic categories which contain them, eliminating the need for rules with long-distance effects. Relations which under previous frameworks had to be accounted for using a number of conditions can be presented in a more succinct and coherent fashion. As in other theories of stress assignment, prosodic phonology relies upon the morphology to provide the underlying forms which are parsed into the prosodic constituents.
1.3.4 Stress in Optimality Theory
In chapter four, building on previous OT treatments (McCarthy & Prince 1993), the stress effects previously modeled in derivational accounts such as Hayes (1995) are treated in an OT framework, using constraints which refer to prosodic constituents. One common English stress pattern described by Hayes (1995), Halle & Vergnaud (1987) and others (see chapter 3) is similar to that generally found in Latin. For trisyllables of this kind, final syllables are treated as extrametrical, and, due to the trochaic form of English feet, stress depends upon the weight of the penult. The contrast is seen between words of the form (LL)s and L(H)s, where ‘L’ and ‘H’ indicate metrically light and heavy syllables respectively, for example —rigin and appŽndix. These can be represented by the following simplified constraint tableaux:
(1.10a)
/origin/
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FtBin
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Non-Fin
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Edgemost
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+ (—ri)gin
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|
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s
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o(r’gin)
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|
!*
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|
o(r’)gin
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!*
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|
s
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(—rigin)
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!*
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*
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|
(1.10b)
/apendiks/
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FtBin
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Non-Fin
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Edgemost
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+ a(pŽn)diks
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|
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s
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a(pen)(d’ks)
|
|
!*
|
|
(‡pen)diks
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!*
|
|
s
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a(pŽndiks)
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!*
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*
|
|
The three constraints used here are parallel to mechanisms used in Hayes (1995). FtBin as formulated in Prince & Smolensky (1993) strictly enforces binary feet, just like Hayes’ bimoraic principle. Violations are incurred by feet which do not contain two (and only two) moras. Non-Finality states that the primary stressed foot cannot be final in the prosodic word, similar to extrametricality. Edgemost, in contrast, demands that the primary stressed foot stands as far to the right edge of the prosodic word as possible, similar to Hayes’ "End Rule: Right". One advantage of the OT account offered here is that the constraint hierarchy formally represents the dependencies between the three constraints via the ranking relationship. In Hayes’ system, the End Rule was said to be unable to "see" the extrametrical syllable, thus the stress would fall near to the right edge of the word, but never upon it. In other cases, however, extrametrical syllables would become visible. Here, there is no "invisibility"; the presence of the final syllable is indicated by the violation of Edgemost seen in the two optimal candidates. It is the higher ranking of Non-Fin which ensures that candidates such as *append’x fail to surface.8
Another advantage of Optimality Theory is that it can explain apparently iterative effects seen in stress assignment without using the iterative rule application required by derivational theories. Constraint rankings can also be used to explain cross-linguistic typologies. Nowhere is this more striking than in the explanation for Hayes’ (1995) typology of stress types, as demonstrated by McCarthy & Prince (1993a), Cohn & McCarthy (1994), and Crowhurst & Hewitt (1995), among others. In chapter four, the framework of Generalized Alignment, introduced by McCarthy & Prince (1993a), is presented. This framework allows for the formal representation of a relationship between two constituents, taking two constituent edges as its arguments. Various orderings of constraints aligning the foot to the prosodic word and vice versa can produce the entire typology of stress patterns described in Hayes (1995).
McCarthy & Prince (1993a: 16) regard the violation of Alignment constraints as "gradient, not Boolean", and quantify violations in terms of each constituent in the universal (first) argument position. Thus, for example, as feet get farther away from the designated aligned edge, they incur more violations of the constraint. This enforces foot-formation in what appears to be an iterative or sequential fashion starting at the designated edge, but which is actually the expression of an alignment constraint within a parallel framework. In addition to the alignment framework, another more general framework for expressing constituent relationships, the No-Intervening constraint of Ellison (1995) and Zoll (1996) is also presented in chapter four, and many descriptive constraints (such as FtBin, Edgemost and Non-Fin) are formalized within using one of these frameworks.
1.3.5 Subcategorization and morphology
All treatments of English stress have needed to refer to morphological structure to account for the stress patterns seen in suffixed words. Some suffixes, those described as "level II" in derivational theories like Lexical Phonology (Kiparsky 1982a, b), behave with regard to stress assignment as if they were not present, e.g., l’mit Ü l’mitless. Other suffixes, described as "level I", appear to participate in the stress assignment of their words, and the suffixed forms take main stress on different syllables than unsuffixed stems, e.g., ‡tom Ü at—mic,’nstrument Ü “nstrumŽntal Ü ’nstrument‡lity. This implies that feet are being applied to these two types in different ways. In chapter four, such differences are captured by subcategorization constraints, which relate prosodic constituents to members of a parallel morphological hierarchy (McCarthy & Prince 1993a, b). This morphological hierarchy consists of items previously used in derivational theories, the morphological word, the stem and the root:
(1.11) The Morphological Hierarchy
MWd
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Stem
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Root
The root is simply a lexical item or morpheme, composed of segments. The morphological word is parallel to the prosodic word and represents a root or series of roots together with all affixes. The stem is a necessary intermediate category. These three constituent types are somewhat analogous to the labels /a, b, g/ used by Inkelas (1989), and provide all the complexity necessary to represent the subcategorization possibilities for English.
Inkelas (1989) uses subcategorization frames to mark lexical items, and each item has two frames, one for morphology and another for phonology. Inkelas adopts the three-level morphological system of Lexical Phonology (the third level being the word level), representing these by the symbols /a, b, g/. An affix like /un-/ would have a morphological subcategorization frame like this (p. 104):
(1.12) un- : [ _ [ ]b ]b
This means that the affix combines with level II items to create a new level II item. The underscore indicates the space that the affix itself would fill (defining it as a prefix) and the inner bracket indicates that it combines with a level II item. Its level I analog /in-/ would have the following frame:
(1.13) in-: [ _ [ ]a ]a
This indicates that it combines with level one items to form another level one item. These frames have the advantage of both accounting for morphological "level" effects as well as explaining why some morphemes only combine in certain ways. For example, "bound" roots like /-ceive/ (p. 66) can be marked to require a level I prefix before they can surface:
(1.14) [ [ ]a ceive ]a
While such a bound root requires a subcategorization frame morphologically, it is no different phonologically from any other stem of its type, and Inkelas does not give it a specific prosodic frame, underlining the potential independence of morphological and phonological structures. Using subcategorization frames, selectional restrictions in either the prosodic or morphological domains may be lexically encoded for the various morphemes which demand them. Subcategorizations of this kind have been reformulated in Optimality Theory as alignment constraints referring to specific affixes (McCarthy & Prince 1993a: 22-4):
(1.15) Align( [um]Af, L, Stem, L)
Here, um- is a Tagalog prefix which aligns to the left edge of a stem. A similar constraint could be expressed for the English prefix /ex-/, expressing its subcategorization for level one stems:
(1.16) Align( [ex]Af, L, Stem, L)
Such a constraint refers, like Inkelas’ subcategorization frames, both to the morphological constituents formed and the directional placement of the affix.
While Inkelas’ system implies that the morphological and phonological constituents tend to correspond, the contents of a morphological constituent being parsed into a prosodic one, she also allows for these constituents to become misaligned. Inkelas uses this proposed misalignment of morphological and prosodic constituents to try to account for extrametricality (p. 151), prefiguring OT alignment constraints. Morphological constituents, like Inkelas’ three constituent levels, are subject to constraints aligning or mis-aligning them with both prosodic constituents and other morphological constituents, allowing for the expression of the full range of constituent patterns found in natural language. Subcategorization constraints of this kind will be used in chapters four, five and six to account for the different behaviors with regard to stress seen between "level I" and "level II" suffixes, as well as between some "level I" suffixes, such as / al/ and / ate/.
Upon application of morphological subcategorization to the data, it becomes clear that most instances of long vowels in complex words occur in monosyllabic stems of the melodic shape /CVC-/ (¤ 4.3). This observation leads to the conclusion that vowels are lengthened in this context due to the combined action of a bimoraic constraint upon feet and an enforced alignment (in certain contexts) of the stem to a foot. In other words, so-called "vowel shortening" is actually indicative of cases where the stem vowel fails to lengthen due to a different stem structure. This solution allows former "lexical exceptions" to shortening rules (e.g., obŽsity, n—tify) to be treated regularly, as showing underlyingly long vowels, while "shortening" vowels (e.g., t—nic, v’lify) are actually underlyingly short, but phonologically lengthened in the contexts where they appear as long (e.g., t—ne, v’le). It also accounts for the otherwise unusual distribution of long and short vowels in lexical stems, wherein long vowels are found plentifully in monosyllables but only rarely in bisyllabic stems (¤ 4.3). Of course, arriving at this solution means abandoning certain long-held ideas about the lexicon, such as the assumption that unsuffixed surface forms are equivalent to the "basic" lexical stem. In the case of alternations like s‡ne Ü s‡nity, it is actually the affixed form s‡nity which is a more faithful indicator of the lexical entry /san/, whose vowel is lengthened in the shorter stem of s‡ne due to minimality constraints.
1.4 Derivation and parallelism
In Optimality Theory as defined by Prince & Smolensky (1993), while rules have been replaced by the constraint hierarchy, the lexicon still plays the same role familiar from derivational theory. An "input" lexical item is presented to Gen, which expands it into all possible well-formed candidates. These are then evaluated by the constraint hierarchy, producing an optimally prosodified "output" surface form. While this entire process can be conceived of as occurring in parallel, rather than through a series of steps, as in the prosodification accounts (e.g., syllabification, foot-formation) of derivational studies such as Hayes (1995), OT nevertheless requires the specification of an "input" item, which will come from the lexicon, presumably via the morphology.
While OT accounts of monomorphemic words can proceed smoothly, avoiding the issue of morphology and referring only to the segments of the lexical item, more complex words require that morphological structure be provided along with the input candidate’s segmental melody. As noted above, various OT analyses, such as Prince & Smolensky (1993), McCarthy & Prince (1993a, b), have proposed constraints which also refer to morphological structures. However, for derivational theories such as Lexical Phonology, morphological complexity meant more than just the presence of structure, it indicated a serial process of word construction which proceeded in discrete stages. This was used to explain both word-formation patterns and structural alternations, such as those ascribed to the cycle. Nothing inherent in OT itself precludes the retention of serial morphological derivation, the Eval process simply replacing the phonological rules of derivational theory. However, this vision of serial derivation carries with it all the problems associated with it from derivational theories, and is based on assumptions about word-formation that are made unnecessary and irrelevant by mechanisms found at the heart of OT. It will be illustrated here that a parallel version of OT can capture the supposed effects of serial derivation, while avoiding its shortcomings.
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